Process Grammar: The Basis of Morphology
Leyton's Process Grammar has been applied by scientists and engineers in many disciplines including medical diagnosis, geology, computer-aided design, meteorology, biological anatomy, neuroscience, chemical engineering, etc. This book demonstrates t
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Michael Leyton
Process Grammar: The Basis of Morphology
Michael Leyton DIMACS Center for Discrete Mathematics and Theoretical Computer Science Rutgers University Busch Campus New Brunswick NJ 08854 USA [email protected]
ISBN 978-1-4614-1814-6 e-ISBN 978-1-4614-1815-3 DOI 10.1007/978-1-4614-1815-3 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2011940966 © Springer Science+Business Media, LLC 2012 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
The Process Grammar has been applied by scientists and engineers in many disciplines, including medical diagnosis (e.g., cardiac diagnosis); geology (e.g., the analysis of volcanic islands); computer-aided design (to establish new CAD operators); meteorology (to analyze weather patterns); biological anatomy (e.g., MRI human brain scans, dental radiographs); engineering bridge design; chemical engineering; etc. The Process Grammar is based on a theorem that I proved in the 1980s called the Symmetry-Curvature Duality Theorem. Researchers have shown that this theorem defines an enormous number of aspects of biology, e.g., anatomy with applications in radiotherapy, surgery, and psychiatry, the tracking of DNA molecules, musculoskeletal development, the morphology of leaves in botany, the morphology of fish, etc; also geology, e.g., for the analysis of drainage patterns, etc; also graphics, e.g., for interactive rendering and cartoon vectorization, etc. The considerable applications of this theorem demonstrate that the theorem is fundamental to morphology. Its importance to morphology is explained by the Process Grammar. In fact, every rule in the Process Grammar is an instance of a rule in a much larger system, my New Foundations to Geometry, that I have elaborated in my book A Generative Theory of Shape (Springer-Verlag, 550 pages). Chapter 2 of the present book gives a brief introduction to these New Foundations, so that the reader is then shown how the Process Grammar is an instance of these New Foundations. The central proposal of my New Foundations to Geometry is that shape is equivalent to memory storage. Therefore, in the New Foundations, geometry is the mathematical theory of memory storage, invented by the New Foundations. This opposes the Standard F
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